His victory over a crowded field on the right stands in contrast to House Majority Leader Eric Cantor's defeat in Virginia's 7th Congressional District, where GOP challenger Dave Brat upset the seven-term Republican for the party's nomination.

But for Graham, any comparison with Cochran was short lived, even though many tea party activists and other grassroots conservatives in South Carolina despise him and other local organizations in the state have censured him in recent years.

Graham had some advantages heading into the contest: He had a massive war chest -- around $8 million cash on hand, which gave him a huge campaign cash advantage over his primary opponents -- and outside groups have steered clear of the race, unlike in Mississippi where establishment and tea party groups fought.

South Carolina Republican consultant Joel Sawyer told CNN that Graham was facing off "against an incredibly weak field of competitors, and of course he benefited by having the 'not Lindsey' vote split among several folks."

"Second, to Lindsey's credit, he ran a great campaign. I think the assumption among a lot of people was that he'd solely wage an air war, but I've been impressed with the way he also ran a traditional, grassroots-focused campaign in addition to a compelling broadcast message. And Lindsey himself spent a lot of time on the ground here holding events and interacting one-on-one with voters," Sawyer added.

Graham debated his opponents for the first and only time this past weekend.

They slammed him over his 2008 vote in favor of the Wall Street bailout, his votes in favor of President Barack Obama's Supreme Court nominations, and especially for his support of immigration reform.

Graham was a member of the bipartisan "Gang of Eight" senators who pushed immigration reform through the chamber last year. The bill was never taken up by the GOP-controlled House.

Heading into Tuesday's contest, polls showed Graham close to the 50% threshold. He spent Monday on a bus tour through the conservative, voter-rich upstate region.

In his final campaign commercial before the primary, Graham touted his conservative credentials, which he said included support for "building the Keystone pipeline, opposing Obamacare, looking for answers on Benghazi, standing up for our military."

And in the ad, which his campaign said was a six-figure statewide buy on TV, radio and digital, Graham said he is a "conservative leader you can count on to get things done."

South Carolina and Virginia were among five states that held primaries on Tuesday.